The analysis of these two distinct approaches is related through corrections to a junction's electronic structure beyond the KS energies for the case of a benzene diamine molecule bonded between two gold electrodes.Using Monte Carlo simulations, we systematically investigate the effect of particle size distribution on the phase behavior of polydisperse hard disks. Compared with the commonly used Gaussian-like polydisperse hard disks [P. Sampedro Ruiz, Q.-l. Lei, and R. Ni, Commun. Phys. 2, 70 (2019)], we find that the phase behavior of polydisperse hard-disk systems with lognormal and triangle distributions is significantly different. In polydisperse hard-disk systems of lognormal distributions, although the phase diagram appears similar to that of Gaussian-like polydisperse hard disks, the re-entrant melting of the hexatic or solid phase cannot be observed in sedimentation experiments. https://www.selleckchem.com/products/Atazanavir.html For polydisperse hard-disk systems of triangle distributions, the phase behavior is qualitatively different from the Gaussian-like and lognormal distributions, and we cannot reach any system of true polydispersity larger than 0.06, which is due to the special shape of the triangle distribution. Our results suggest that the exact particle size distribution is of primary importance in determining the phase behavior of polydisperse hard disks, and we do not have a universal phase diagram for different polydisperse hard-disk systems.We studied spectroscopic signatures of the nonadiabatic dynamics at conical intersections formed by the lowest excited singlet states in pyrazine. We considered two ab initio models of conical intersections in the excited states of pyrazine developed by Sala et al. [Phys. Chem. Chem. Phys. 16, 15957 (2014)] a two-state (B2u and B3u), five-mode model and a three-state (B2u, B3u, and Au), nine-mode model. We simulated the signals of three widely used techniques time- and frequency-resolved fluorescence spectroscopy, transient absorption pump-probe spectroscopy, and electronic two-dimensional spectroscopy. The signals were calculated through third-order response functions, which, in turn, were evaluated with the numerically accurate multiple Davydov ansatz. We establish spectroscopic signatures of the optically dark Au state and demonstrate that the key features of the photoinduced dynamics, such as electronic/nuclear populations, electronic/nuclear coherences, and electronic/nuclear energy transfer processes, are imprinted in the spectroscopic signals. We show that a fairly complete picture of the nonadiabatic dynamics at conical intersections can be obtained when several spectroscopic techniques are combined. Provided that the time resolution is sufficient, time- and frequency-resolved fluorescence may provide the best visualization of the nonadiabatic dynamics near conical intersections.A method to optimize a conformational pathway through a space of well-chosen reduced variables is employed to advance our understanding of protein conformational equilibrium. The adaptively biased path optimization strategy utilizes unrestricted, enhanced sampling in the region of a path in the reduced-variable space to identify a broad path between two stable end-states. Application to the inactivation transition of the Src tyrosine kinase catalytic domain reveals new insight into this well studied conformational equilibrium. The mechanistic description gained from identifying the motions and structural features along the path includes details of the switched electrostatic network found to underpin the transition. The free energy barrier along the path results from rotation of a helix, αC, that is tightly correlated with motions in the activation loop (A-loop) as well as distal regions in the C-lobe. Path profiles of the reduced variables clearly demonstrate the strongly correlated motions. The exchange of electrostatic interactions among residues in the network is key to these interdependent motions. In addition, the increased resolution from an all-atom model in defining the path shows multiple components for the A-loop motion and that different parts of the A-loop contribute throughout the length of the path.We present an analytic description of doubly resonant infrared-visible sum (SFG) and difference frequency generation (DFG) spectroscopies. Within the Born-Oppenheimer and Condon approximations for harmonic oscillators, we extend the usual theory, limited to linear electron-vibration coupling, and introduce the quadratic coupling phenomena (mode distortion and mode mixing) in the excited state. The excitation spectra of vibrations in SFG and DFG experiments are calculated in integral form for arbitrary mode distortions and small amplitude mode mixing between pairs of modes. Mode distortion modifies all orders of vibronic coupling including the fundamental process, whereas mode mixing appears as a perturbation added to the distorted mode case. For small quadratic coupling amplitudes, the results may be recast in simple analytic forms after the introduction of the overlap spectral function and developed in sums and products of Lorentzian functions.Dynamics are fundamental to all aspects of chemistry and play a central role in the mechanism and product distribution of a chemical reaction. All dynamic processes are influenced by the local environment, so it is of fundamental and practical value to understand the structure of the environment and the dynamics with nanoscale resolution. Most techniques for measuring dynamic processes have microscopic spatial resolution and can only measure the average behavior of a large ensemble of sites within their sampling volumes. Tip-enhanced Raman spectroscopy (TERS) is a powerful tool for overcoming this limitation due to its combination of high chemical specificity and spatial resolution that is on the nanometer scale. Adapting it for the study of dynamic systems remains a work in progress, but the increasing sophistication of TERS is making such studies more routine, and there are now growing efforts to use TERS to examine more complex processes. This Perspective aims to promote development in this area of research by highlighting recent progress in using TERS to understand reacting and dynamic systems, ranging from simple model reactions to complex processes with practical applications.